This is the webpage for the Fall 2018 class SC/MATH 1019B taught by John Machacek.
The course meets Tuesday and Thursday from 11:30am to 1:00pm in Vari Hall Room B.
For essential information about the course please see the course outline.
Some information from the course outline is reproduced below for convience.
Homework assignments as well as solutions to homework assignemtns and tests can also be found below.
If you purchased the ebook through the York University Bookstore you need to go to
https://connect.mheducation.com/class/j-machacek-math-1019-section-b
to access the ebook.
Here are some slides hinting at some of the many applications of discrete mathematics.
Instructor: John Machacek
Office: 2025 DB (Victor Phillip Dahdaleh Building)
Office hours: Tuesday 1:15pm - 2:15pm, Thursday 10:00am - 11:00am
Email: machacek@yorku.ca
| Test 1 | Oct. 2 | Solutions for Test 1A and Solutions for Test 1B |
| Test 2 | Nov. 1 | Solutions for Test 2 |
| Test 3 | Nov. 29 | Solutions for Test 3 |
| Final exam | Dec. 16 (Sunday) at 14:00 in LAS B, LAS C |
| Homework 1 | Sep. 20 | Solutions |
| Homework 2 | Oct. 23 | Solutions |
| Homework 3 | Nov. 20 | Solutions |
| Homework 4 | Dec. 4 |
| Sep. 6 | Propositional logic | |
| Sep. 11 | Propositional equivalences and quantifiers | |
| Sep. 13 | Inference and proof | |
| Sep. 18 | More proofs | Extra on proof by contradiction |
| Sep. 20 | Sets | |
| Sep. 25 | Sets operations | Interval activity |
| Sep. 27 | Review for Test 1 | |
| Oct. 4 | Functions | |
| Oct. 16 | More functions | |
| Oct. 18, Oct. 18b | Sequences and sums, cardinality | |
| Oct. 23 | Big-O | |
| Oct. 25 | Induction | |
| Oct. 30 | Review for Test 2 | |
| Nov. 6, Nov. 6b | Recursion | |
| Nov. 8 | Solving recurrence relations | |
| Nov. 13 | Equivalence relations | |
| Nov. 15 | Equivalence relations and partitions | |
| Nov. 20 | Graphs | Extra on bipartite graphs |
| Nov. 22 | Graph coloring | |
| Nov. 27 | Review for Test 3 | |
| Dec. 4 | Review for Final Exam |
Below are some additional exercises for practice. Problem numbers are taken from the 8th Edition. If you have a different edition exercise numbers might differ. As a general rule, any exercise that resembles something we did or discussed in class is good for practice. Sometimes many exercises are listed, but there are only a couple "types" in each section. I recommend trying enough of each "type" until you feel comfortable, exactly how many will vary by student.
Here are problems for sections covered on Test 1.
| Section | 8th Edition |
| 1.1 Propositional Logic | #29 - #41 |
| 1.3 Propositional Equivalences | #9 - #12, #17 - #37 |
| 1.4 Predicates and Quantifiers | #1, #2, #11 - #16, #35 - #38 |
| 1.5 Nested Quantifiers | #26 - #28, #30 - #35 |
| 1.6 Rules of Inference | #23, #24, #27 - #29 |
| 1.7 Introduction to Proofs | #1 - #6, #16 - #20 |
| 1.8 Proof Methods and Strategey | #1 - #6, #31 - #34 |
| 2.1 Sets | #11 - #13, #19 - #29, #32 - #44 |
| 2.2 Sets Operations | #5 - #17, #32 - #37, #53, #54 |
Here are problems for sections covered on Test 2.
| Section | 8th Edition |
| 2.3 Functions | #8 - #23, #33 - #37, #42, #43 |
| 2.4 Sequences and Summations | #1-#4, #12 - #17, #29, #33, #36, #39-#42 |
| 2.5 Cardinality of Sets | #1 - #11, #28 |
| 3.2 The Growth of Functions | #1 - #24 |
| 5.1 Mathematical Induction | #3 - #23 |
| 5.2 Strong Induction and Well-Ordering | #3 - #8 |
Here are problems for sections covered on Test 3.
| Section | 8th Edition |
| 5.3 Recursive definitions and Structural Induction | #36 - #44, #53 - #57 |
| 8.1 Applications of Recurrence Relations | #7 - #18 |
| 8.2 Solving Linear Recurrence Relations | #1 - #4, #11 - #15 |
| 8.3 Divide-and-Conquer Algorithms and Recurrence Relations | #6 - #13 |
| 9.1 Relations and Their Properties | #1 - #17 (you will need to look in the book for the definition of "antisymmetric") |
| 9.5 Equivalence Relations | #1 - #3, #11 - 16, #43 - #46 |
| 10.8 Graph Coloring | #5 - #16 |